Nash equilibria

In developing countries undergoing liberalising economic reforms, there are typically local incumbents facing the loss of protection. Strategic lobbying by such firms for a price-capping regulatory regime is, under certain conditions, one way in which they can deter entry by competitors who are likely to be foreign firms. We show that a regulatory price can be set such that the net profit of the entrant is lower than the entry cost thus deterring entry. We then show that it is possible for the profit of the incumbent to be greater under regulation which deters entry than under unregulated duopoly. Counter-intuitively, we further discover that lobbying for regulation is to be expected where the incumbent firm is relatively cost-efficient. Finally, we consider the case of multiple incumbents threatened by entry. We observe a co-ordination problem and consider the possibility of co-operation in lobbying. We then show that such co-operation, if possible, is always preferable to non-co-o...

We analyze a one-shot experiment on the traveler's dilemma in which members of the Game Theory Society, were asked to submit both a (possibly mixed) strategy and their belief concerning the average strategy of their opponents. Very few entrants expect and play the unique Nash equilibrium, while we observe a fifth playing the cooperative solution of the game, i.e. a

A special case of dollarization is analyzed: quotation of prices in dollars. The proposed explanation is price stickiness: when price adjustment is costly, forms can prefer to fix their prices in a stable foreign currency rather than in an unstable domestic one in order to avoid frequent price changes. The proposed model shows how the choice of price-setting currency made by a firm depends on the in ation rate, exchange rate volatility, the pricing currency of competitors and input suppliers, and the shape of the demand function. The model predicts that there are two Nash equilibria in the economy populated by symmetric firms: an equilibrium with uniform ruble pricing and an equilibrium with uniform dollar pricing. It is shown that in economy with less competition a smaller increase in inflation is needed to make an individual firm deviate from the equilibrium with uniform ruble pricing and turn to pricing in dollars.

ABSTRACT In this paper we focus on the maximization of the information rates subject to transmit power constraints for noncooperative multiple-input multiple-output (MIMO) systems, using the same physical resources, i.e., time, bandwidth and space. To derive decentralized solutions that do not require any cooperation among the systems, the optimization problem is formulated as a static noncooperative game. The analysis of the game for arbitrary MIMO interference channels is quite involved, since it requires the study of a set of nonlinear nondifferentiable matrix-valued equations, based on the MIMO waterfilling solution. To overcome this difficulty, we provide a new interpretation of the waterfilling operator, for the general MIMO multiuser case, as a matrix projection. This key result allows us to simplify the study of the game and to obtain sufficient conditions for both uniqueness of the Nash equilibrium (NE) and convergence of the proposed totally asynchronous distributed algorithms. The proposed approach provides a general framework that encompasses all previous works, mostly concerned with the particular case of SISO Gaussian frequency-selective interference channel.

Car use is an increasingly serious problem in many modern cities because of polluting emissions, noise, accidents and congestion. To examine this issue, this paper analyzes the individual choice between taking the car and using alternative transport modes (e.g. walking, cycling, taking the bus etc.) in the presence of cars’ negative impacts on alternative transport modes. Using a simple evolutionary model, we show the existence of suboptimal Nash equilibria characterized by the widespread use of cars and discuss the effects of simple transport policies that reduce cars’ negative impacts on alternative transport modes.

We consider non cooperative games in all-optical networks where users share the cost of the used ADM switches for realizing given communication patterns. We show that the two fundamental cost sharing methods, Shapley and Egalitarian, induce polynomial converging games with price of anarchy at most 5/3, regardless of the network topology. Such a bound is tight even for rings. Then, we show that if collusion of at most k players is allowed, the Egalitarian method yields polynomially converging games with price of collusion between ${{3}\over{2}}$ and ${{3}\over{2}}+{{1}\over{k}}$ . This result is very interesting and quite surprising, as the best known approximation ratio, that is ${{3}\over{2}}+\epsilon$ , can be achieved in polynomial time by uncoordinated evolutions of collusion games with coalitions of increasing size. Finally, the Shapley method does not induce well defined collusion games, but can be exploited in the definition of local search algorithms with local optima arbitrarily close to optimal solutions. This would potentially generate PTAS, but unfortunately the arising algorithm might not converge. The determination of new cost sharing methods or local search algorithms reaching a compromise between Shapley and Egalitarian is thus outlined as being a promising and worth pursuing investigating direction.

We consider two min–max problems (1) minimizing the supremum of finitely many rational functions over a compact basic semi-algebraic set and (2) solving a 2-player zero-sum polynomial game in randomized strategies with compact basic semi-algebraic sets of pure strategies. In both problems the optimal value can be approximated by solving a hierarchy of semidefinite relaxations, in the spirit of the moment approach developed in Lasserre (SIAM J Optim 11:796–817, 2001; Math Program B 112:65–92, 2008). This provides a unified approach and a class of algorithms to compute Nash equilibria and min–max strategies of several static and dynamic games. Each semidefinite relaxation can be solved in time which is polynomial in its input size and practice on a sample of experiments reveals that few relaxations are needed for a good approximation (and sometimes even for finite convergence), a behavior similar to what was observed in polynomial optimization.

We study the performance of approximate Nash equilibria for congestion games with polynomial latency functions. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor ε. We give tight bounds for the price of anarchy of atomic and non-atomic congestion games and for the price of

This paper studies a decentralised job market model where firms (academic departments) propose sequentially a (unique) position to some workers (Ph.D. candidates). Successful candidates then decide whether to accept the offers, and departments whose positions remain unfilled propose to other candidates. We distinguish between several cases, depending on whether agents’ actions are simultaneous and/or irreversible (if a worker accepts an

Evolutionary game theory provides an answer to two of the central questions in economic modeling: when is it reasonable to assume that people are rational? And, when is it reasonable to assume that behavior is part of a Nash equilibrium (and if it is reasonable, which equilibrium)? The traditional answers are not compelling, and much of evolutionary modeling is motivated by the need for a better answer. Evolutionary game theory suggests that, in a range of settings, agents do (eventually) play a Nash equilibrium. Moreover, evolutionary modeling has shed light on the relative plausibility of different Nash equilibria.

We investigate the effectiveness of Stackelberg strategies for atomic congestion games with unsplittable demands. In our setting, only a fraction of the players are selfish, while the rest are willing to follow a predetermined strategy. A Stackelberg strategy assigns the coordinated players to appropriately selected strategies trying to minimize the performance degradation due to the selfish players. We consider two orthogonal cases, namely linear congestion games with arbitrary strategies and congestion games on parallel links with arbitrary non-negative and non-decreasing latency functions. We restrict our attention to pure Nash equilibria and derive strong upper and lower bounds on the Price of Anarchy under different Stackelberg strategies.

In most work on multi-player game theory, payoffs are rep- resented in tabular form: if n agents play a game in which each player has (say) two actions available, the game is given by n matrices, each of size 2 n , specifying the pay- offs to each player under any possible ...

We show that a proper equilibrium of a matrix game can be found in polynomial time by solving a linear (in the number of pure strategies of the two players) number of linear programs of roughly the same dimensions as the standard linear programs describing the Nash equilibria of the game.

This paper provides a simple formula describing all Nash equilibria in symmetric monotone singleton congestion games. Our approach also yields a new and short proof establishing the existence of a Nash equilibrium in this kind of congestion games without invoking the potential function or the nite improvement property.

This paper investigates a relatively new direction in Multiagent Reinforcement Learning. Most multiagent learning techniques focus on Nash equilibria as elements of both the learning algorithm and its evaluation criteria. In contrast, we propose a multiagent learning algorithm that is optimal in the sense of finding a best-response policy, rather than in reaching an equilibrium. We present the first learning algorithm that is provably optimal against restricted classes of non-stationary opponents. The algorithm infers an accurate model of the opponentýs non-stationary strategy, and simultaneously creates a best-response policy against that strategy. Our learning algorithm works within the very general framework of n-player, general-sum stochastic games, and learns both the game structure and its associated optimal policy.

We use game theory and Santa Fe Artificial Stock Market, anagent-based model of an evolving stock market, to study theoptimal frequency for traders to revise their market forecastingrules. We discover two things: There is a unique strategic Nashequilibrium in the game of choosing forecast revision rates, andthis equilibrium is sub-optimal in the sense that traders'earnings are not maximized an the